Ugh, reminds me, I don't think the drums' cymbals would be loud enough without amplification, so we do need those in the PA as well.
The cymbals should be the least of your worries. Except maybe the hi-hit, you'll want that coming through.
You can carry a show just fine without people hearing every cymbal crash. OTOH if kick drum and bass are lacking your band will come off sounding lame.